Physicochemical interpretation of molecular connectivity indices

Molecular connectivity indices are identified as components of the molecular accessibility. The first- and second-order connectivity indices represent molecular accessibility areas and volumes, respectively, whereas higher order indices represent magnitudes in higher dimensional spaces. In identifying accessibility perimeters, we recognized the atom degrees as a measure of the accessibility perimeter of the corresponding atom. The Randic and connectivity indices are identified as the two components of the molecular accessibility area. The accessibility perimeter is computed here from the van der Waals and covalent radii of the atoms and the overlapping angle between the van der Waals circumferences of bonded atoms. The description of the accessibility area in terms of the first-order Randic and connectivity indices accounts for the success of these descriptors in correlating different physicochemical and biological properties because they are a measure of the extension of intermolecular interactions. A theoretical justification for the selection of the exponent in the Randic invariant is provided by the relation between the valence degree and the accessibility perimeters calculated in this work.